The logs rules work "backwards",
so you can simplify ("compress"?) log expressions. When they
tell you to "simplify" a log expression, this usually means
they will have given you lots of log terms, each containing a simple argument,
and they want you to combine everything into one log with a complicated
argument. "Simplifying" in this context usually means the opposite
of "expanding".

Simplify log2(x)
+ log2(y).

Since these logs have
the same base, the addition outside can be turned into multiplication
inside:

Then I'll account for
the subtracted term by combining it inside with division:

You can use the Mathway widget below to
practice simplifying a logarithmic expression. Try the entered exercise,
or type in your own exercise. Then click "Answer" to compare
your answer to Mathway's. (Or skip the widget and continue
with the lesson.)

(Clicking on "View Steps"
on the widget's answer screen will take you to the Mathway site, where
you can register for a free seven-day trial of the software.)